Friday, August 22, 2014

The Money Multiplier

Update: Please read comments, as I often learn that I am still learning.

Update 2: see here.

I have received more than one kind and gentle email due to my post entitled “Austrian View of Fractional Reserve Banking: Tamny Mostly Right, Shedlock Mostly Wrong.”  The emails raise an objection to the following from that post:

Tamny: To Austrians, fractional banking leads to “excess credit creation” through what they refer to as a “money multiplier.”

The problem is that the very notion of a “money multiplier” is a logical impossibility; one that dies of its illogic rather quickly if analyzed in the lightest of ways. To explain what isn’t, banks are generally required to keep a 10% deposit cushion. Simplified, if a bank is the recipient of a $1,000 deposit, it can generally only lend out $900, or 90% of its deposits. What might surprise some is that the previously described loan is what has many Austrians up in arms.

To which I wrote in that post:

Please read the preceding again.  $1000 doesn’t become $10,000.  In fact, on prudently calculated reserves, $1000 doesn’t become more than $1000 in any economically meaningful sense.  The bank is confident in lending out $900 because it believes the depositor will not demand more than $100 from his deposit. (Emphasis added.)

It is interesting: the two individuals – the initial depositor and the subsequent borrower – hold two accounts totaling $1900.  But digits on paper aren’t excess credit creation in any economically meaningful sense of the term. (Emphasis added.)

I will preface my comments with the following: First, fractional reserve banking as practiced today is not fraud.  Second, markets are perfectly capable to regulate excess leverage at financial institutions.  I will not expand on either of these here as I have written on each topic more times than I can count.  These are not the primary purpose of this post; I only introduce these to clarify the baseline from where I will begin my analysis.

Given these two points (not fraud, markets capable of regulating leverage ratios), I lose interest quickly on the topic of proper banking / money / credit / currency issues.  If the market is capable of handling the issue, anything more I might write about it suggests central planning – one reason it strikes me that advocates of a 100% gold-backed standard are central planning.

As I do not think much further about the topic, it behooves me to consider that my statement in the earlier post might not be well thought through – as suggested by the emails.  The emails I have received come from multiple individuals whom I consider quite well versed on such matters; therefore it seems to me prudent to see if my statement holds water.

With that, let’s begin:

  • Depositor A deposits $1000 at Bank A.
  • Bank A, having previously calculated a prudent reserve ratio, determines it can lend $900 of these funds to Borrower 1.
  • Borrower 1 now acting as Depositor 1, deposits $900 in Bank B.
  • Bank B, again calculating prudently, loans $810 to Borrower 2.
  • Borrower 2 now acting as Depositor 2, deposits $810 in Bank C.
  • Prudent Bank C loans $729 to Borrower 3.
  • Borrower 3, as Depositor 3, deposits $729 in Bank D.

And so on….

You get the idea.

There are four depositors in my example; in total, they have deposited $3439 – far more than the initial $1000 deposit.  They each hold account statements that, when summed together – equal $3439.  If I continue the example, the sum of the account statement totals would be $10,000 – no surprise.  As best as I understand Rothbard and those who point to this fact – a fact I do not dispute – this is the crux of the issue.

Now, why do I emphasize “prudent” reserve ratios?  Simply to not muddy the example with poor business judgment on the part of bank management.  Poor judgment by an entrepreneur might be cause for insolvency, but not a cause to ban the practice (do we really want to initiate force to ban what some might consider an imprudent business arrangement?).

So, in my example, prudent bank reserve ratio means Depositor A never draws more than $100 from his balance – he draws some, he adds some – but overall it fluctuates around the $1000 initially noted on his account statement.  Same for Depositors 1, 2, & 3 with their respective balances.

So, Depositor A never draws more than $100; Depositor 1 never draws more than $90; Depositor 2 never more than $81.  My example ends there, but if extended all the way to Depositor N (100 is more than enough), exactly $1000 is drawn in total by all 100 depositors at any one time – the same $1000 initially deposited.

Now, I admit the example is simple – each bank likely has hundreds or thousands of depositors – all that matters is the prudence of the aggregate ratio (and with larger numbers, the risk of error would seem to be reduced); individual banks on a day-to-day basis will likely move above or below the target ratio (after all, the withdrawal from one bank often gets deposited into a different bank) – but, if prudently calculated, this is why there is some reserve (in my example, 10%) to offset this risk.  Adjustments can be made over time if the overage or underage persists.

So, the math is correct, as depicted by Rothbard.  But the implications are incorrect: not all $10,000 can be spent at the same time – only $1000 can. 

“But,” you exclaim, “what if more than $1000 is demanded at once?”

It is beyond the purpose of this post to answer this question in any detail, but I offer a hint: other than cash withdrawals (a tiny fraction of the modern economy), every withdrawal in one place is a simultaneous deposit in another – therefore, privately-agreed-upon interbank transfer agreements will mitigate this risk; if this proves insufficient for any individual, grossly imprudent bank – bankruptcy.  In either case, the problem will be resolved and assets will transfer to entities as decided by contract and bankruptcy court.  But to avoid diving too far down the path of another issue, suffice it to say that I see no Austrian or libertarian reason to insert monopoly force in order to mitigate the risk of poor entrepreneurial judgment.

In summary, there is not more in circulation than the amount initially deposited.  I have a sense that this is economically meaningful.

Maybe I am wrong about all of this: If I am wrong in my conclusion, I welcome comments as to why and why it matters (don’t say “inflation”: you have a right to your property; you have no right to the value of your property).  Also, I welcome comments about what might be done about it – while respecting free markets, private contracts, the NAP, and private property.


  1. I agree with you bionic mosquito that there are no consequences of this rise in the overall money supply (when demand deposits are included) that comes anywhere close to requiring any kind of central planning or regulation. The free market is fully capable of disciplining any imprudent banks. I see no fraud and the markets are fully capable of regulating leverage ratios. Simply put, I agree with you.

    So let me merely address the more arcane matter of whether more than the original $1000 can circulate under this scenario. I say that it can.

    I will use a fairly artificial model to show how this can happen. There are many more possibilities, but I show this extremely simplistic example just to show the point.

    In your example, we arrived at 4 banks: A, B, C, D.

    Imagine the simple construct whereby it just so happens that the various banks clients do business with each other, but in a very balanced fashion. The time period doesn’t matter, could be every day, or every week, doesn’t matter. But imagine that the pattern of the business that all 4 banks transact results in *each* bank having a combined total of $500 drawn against it during each time period. That’s $500 from bank A, B, C, D. Furthermore, imagine that each bank also receives deposits of $500 from the other banks during that same time period.

    Here we have a very balanced model, and just enough to show the principle. In each time period, the combined customers of all 4 banks are able to “spend” a total of *$2000*, ($500 from each bank). As luck would have it in this balanced system each bank receives back the $500 as deposits from the other banks — or more likely the transactions simply cancel each other out and no funds are transferred at all. This from an original deposit of $1000.

    My contention all along has NOT been that FRB is illegitimate, or fraud, or in need of regulation or central planning or some authority. I believe that the market would work in this area just great, and I do mean the FREE market.

    My original contention was simply that when Tamny stated that “The problem is that the very notion of a “money multiplier” is a logical impossibility” he was simply wrong.

    My further contention is that there are at least SOME consequences of fractional reserve banking upon the money supply. Consequences that economists might like to be aware of.

    NOTHING, however that comes close to justifying a non-free banking system. Do not mistake my quibbling over the money multiplier effect as in any way endorsing a non-free market in banking services.

    The market will handle all of this just fine.


    1. gpond

      This sounds more like a velocity issue. In my example, I offered that the reserve ratio was not crossed - that is, Depositor A doesn't reduce his balance below $900; instead his balance fluctuates around the $1000 mark, sometimes more, sometimes less.

      In one week, Depositor A could do five spending transactions of $100 each and five deposit transactions of $100 each (I believe this conforms to both your model and mine).

      In this case, nothing changes in my outline - and the thresholds I identified are not crossed.

      Velocity (as the term is used) is another issue.

      Am I missing something?

    2. No, I don’t think you are missing anything.

      To quibble any more would just be, well.. quibbling. What is or is not economically significant may be determined in part by one’s interest level in economics.

      I was an early adopter of your position, BM, that in a truly free market there should be no mechanism to outlaw freely entered contracts, including FRB. The market is the best mediator of that. That said, even the free market will not be perfect, nor should we expect it to be, nor should we attempt to centrally plan it into perfection. At least it is self-correcting.

      By way of analogy, let me paraphrase Robert Higgs, as I can’t find his exact quotation but he once said something like this: When people ask me what would life be like in an anarchist society I tell them, well it would probably be pretty terrible, maybe even horrible… Just not as bad as this.

    3. Somewhere I read a quote from Mises; I, too,will paraphrase.

      When asked how we escape inflation, Mises replied "death." He didn't say "free markets," although, like Higgs, I might retort "just not as bad as this."

      Thank you for pushing me on this.

    4. Regarding the question of life under anarchy, another great man of wisdom may have had some insight:

      "I ain't promising you nothing extra. I'm just giving you life and you're giving me life. And I'm saying that men can live together without butchering one another."

  2. As usual, I continue to research this issue, mainly to figure out if I have been wrong. In that search, I found a rather balanced and cogent critique of Tamny's positions. Believe me, I found some that were not. See here:

    The whole article is worth a read, but I'll give one short quotation:

    So is M1 really money? Most definitely, because it fits the definition perfectly: a generally accepted medium of exchange. Is there anyone reading this piece who does not keep much more of his money in a checking account than in cash? How often do we pay cash these days? We use our debit cards, paper checks, or on-line transfers instead of currency. Or we use credit cards which we pay off by on-line transfer or check. All this is M1 money, all created by private banks under the aegis of fractional reserve banking. Notwithstanding the problems cited above, it all works rather well.

  3. This might have been a better quotation to capture the spirit of the Tamny critique I posted, however I provide the other quotation because it sounded as if I had written it myself. :)

    As Tamny says, it is only some Austrians who have a problem with fractional-reserve banking. I consider myself an Austrian but I do not share the view of fractional reserves of the Mises Institute contingent, whom I prefer to call hard-money advocates.

    The alleged problem, as the hard money people have it, is that under fractional reserves it appears that two people have a claim on the same dollar. This, they say, is fraud. But it is not fraud if the arrangement is disclosed to all parties. There are problems with our present-day fractional-reserve system, which I discuss below, but fraud is not one of them. (Incidentally, Tamny scores a point when he wonders about the hard money people calling in the state to crush the alleged fraud, but I believe most of them are anarchists and would have private protection agencies do the job. Just how this might work is beyond me.)

    1. gpond, this is very helpful for me:

      I think I went further with the following statement than I am qualified to go:

      “In summary, there is not more in circulation than the amount initially deposited.”

      Fortunately, I covered my backside:

      “Maybe I am wrong about all of this: If I am wrong in my conclusion, I welcome comments as to why and why it matters (don’t say “inflation”: you have a right to your property; you have no right to the value of your property).”

      The subject article, if I understand the author correctly, answered the “why.” At least the author and I seem to agree that there is nothing to be done about it beyond market forces.

      Therefore I should have left well enough alone, with the following position:

      “I will preface my comments with the following: First, fractional reserve banking as practiced today is not fraud. Second, markets are perfectly capable to regulate excess leverage at financial institutions.”

      I will stick to this, it is enough for my purposes.

  4. What if depositor withdraws his $1000 immediately after bank has lent out $900. Where does bank get money to repay depositor? I hope you don't answer from the government.

    1. This is answered in the post, immediately after I pretend I am a commenter, like you, asking the following question: "“But,” you exclaim, “what if more than $1000 is demanded at once?”

      Let me know if you require further clarification.

    2. Well , regardless whether the cash is withdrawn or not , the fact is that both depositor and borrower can write a check over those $ 900.-.
      So the question is how that does not distort the perceived social time preference?

  5. I am more confused now than before.What about check money ?I understood that commercial banks could make up to 10(or what ever ratio was) On to p of deposits?What article do i need to read to understand?I have read Jeckle
    Island and most any thing on fractional reserve banking.But I odviously don't understand

    1. cowboy, please do not let anything I wrote in this post add to (or cause) any confusion. As I wrote in the update, I went to far on this one point. I should have just stuck to my views on FRB.

    2. Article is great for conjuring dialectic, abstract thinking.
      As libertarians we are at disadvantage.We have to be armed to the
      teeth with knowledge and facts in so many areas.From money to medicine to be able to make palatable arguments.Just want to make sure I am on the right path.I wasn't for a long time.
      I think to my self now "Gee why didn't Rush Limbaugh and so many other cornballs I used to listen to explain this stuff to me?"I remember watching (2007) the 45 minute youtube clip that Lew Rockwell and Mises made about the federal reserve.
      It blew my mind!!!I had no idea how it all worked!!!I bet I sat there for twenty minutes letting it all soak in.It was like seeing naked pictures of you grandma.The short documentary was just enough to change my whole life.Now I have a insatiable appetite
      to re learn all I can.Thanks so much for what you'do!!!!

    3. thank you for this; it will take me a while to recover....

  6. This comment is only to provide a link to a discussion with an "FRB is fraud" commenter, found here:

    The pertinent comment: “All banks in the US include however a clause in the depositors contract that specifically says that the relationship between the depositor and the bank is exclusively one of creditor/debtor.”

    My reply: ...That you can write these words and still describe it as fraud baffles me. There is no point to continue this discussion.